soundtrack - How is it decided which parts of a movie need background music?

As there are no hard and fast rules for the use of music in filmmaking, this question runs the risk of becoming conversational rather than providing a succinct answer.

That said, I am in the middle of finalizing the score on my latest short animated film - so I'll share my reasoning for the inclusion of the background music in the hope that it answers your question.

While working with my composer, I had several motives in mind for the
musical cues he delivered.

Firstly, music (and sound design in general) are a vital part of the
overall film language (with some exceptions - see The Artist, et al
;)), and I needed musical cues that highlighted the emotional impact
of certain scenes. There are moments of high tension, comedy and
sadness in the film, and my composer has enhanced these moments
dramatically by reinforcing the rhythm of the edits and also providing
a 'pointer' for the audience as to how they should be feeling at any
given time. Music is a very powerful tool for controlling your
audience's feelings.

Secondly, I instructed him to create a series of leitmotifs for
the characters in the film. This is a technique used most famously by
John Williams in the Star Wars saga, whereby each character has
their own theme which reoccurs throughout the films, albeit in
different styles, reflecting the characters' current state of
mind/situation/interaction with others. Look at Vader's theme. Heavy
brass through the original trilogy, and then played on a harp as he
dies - beautiful and deeply moving. For my film, I have a main
character who is the antagonist (villain) of the piece, and is at odds
with the other characters. For this reason, I had his theme not only
jar against the rest of the soundtrack, but it becomes strained and
unravels as he becomes more dangerous during the film's progression.

I also asked my composer to create a theme for the landscape (there is
mountain climbing involved), and we used this opportunity to include
ethnic instruments that reinforce the geography and the nationality of
the protagonists. So we ended up with an epic score that sounds like
Max Steiner's King Kong soundtrack with elements of Tibetan
woodwinds and thumb cymbals woven in!

This is just the tip of the iceberg when it comes to music decisions,
but I hope it gives you a good starting point in answer to your
question.